Aspects of Potential Vorticity Fluxes: Climatology and Impermeability

Abstract

Abstract Some aspects of the dynamics of generalized potential vorticity (PV) density P = ω ⋅ ∇χ are discussed with the main emphasis on P fluxes, where ωa is absolute vorticity and χ is a scalar. The impermeability theorem claims that there is no net P flux across a χ surface. Various forms of the flux are presented that mostly cross χ surfaces. As these fluxes are as dynamically relevant as the one chosen for the theorem, P fluxes through a surface element are inherently multivalued and there is no best choice on physical grounds. Nevertheless, the net P flux is unique for closed surfaces. This point is illustrated by P integrals over the volume between the earth’s surface and an isentropic surface. Reanalysis data are used to present mean advective and some nonadvective P fluxes for χ = θ in height coordinates. The extratropical tropopause appears to be supported by advective P fluxes. A satisfactorily closed P budget cannot, however, be presented.